High-resolution time-frequency analysis method based on parametric resampling

Abstract

A high-resolution time-frequency analysis method based on parametric resampling calculates the relative fluctuation spectrum of the input signal, extracts the ridge line from it to estimate the relative trend function, then expresses the parametric resampling function with the kernel function obtained by fitting the relative trend function, and then performs time-frequency analysis based on the resampling function to obtain the high-resolution time-frequency distribution of the multi-component non-stationary signal. The present invention can extract the relative trend shared by multiple component components from a complex multi-component signal, thereby realizing parametric resampling time-frequency analysis, and can simultaneously improve the time-frequency resolution of each component, and is not disturbed by densely adjacent complex components, has good anti-noise performance, and can obtain accurate and high-resolution time-frequency distribution.

Description

Technical Field

[0001] The present invention relates to a technology in the field of signal processing, in particular to a time-frequency analysis method for non-stationary signals such as mechanical vibration and sound, specifically a time-frequency analysis method based on parametric resampling, in which the frequency resolution can reach the frequency resolution of discrete Fourier transform of stationary signals, and the time resolution reaches the sampling time interval. Background Art

[0002] A large number of signals in production and life are non-stationary signals, such as the vibration signal of rotating mechanical equipment during the speed increase and decrease stage, the frequency distortion of sound signals caused by the Doppler effect, and the non-stationary sound signals emitted by organisms, etc. In order to realize the analysis of non-stationary signals, it is often necessary to provide a joint distribution analysis of the signal in the time domain and the frequency domain, that is, the time-frequency analysis of the signal. According to whether the parameters of the time-frequency atoms are related to the signal, the time-frequency analysis can be divided into two categories: parametric time-frequency analysis and non-parametric time-frequency analysis. Commonly used time-frequency analysis methods such as short-time Fourier transform, wavelet transform, and Wigner distribution are all non-parametric time-frequency analysis methods. Because the time-frequency atoms do not match the signal, they have low time-frequency resolution or are seriously interfered by cross terms. The parametric time-frequency analysis method uses a parametric kernel function to construct atoms that match the time-frequency characteristics of the analyzed signal, which can effectively improve the time-frequency resolution of the time-frequency analysis. Such as the widely used linear frequency modulation wavelet transform, and nonlinear frequency modulation wavelet transform, etc. The existing technology demodulates the original nonlinear frequency modulation component to improve the resolution by constructing atoms that conform to the time-frequency distribution of a certain signal component. However, the demodulation operation can only target a certain frequency component. For multi-component signals such as sound signals and vibration signals, the time-frequency resolution of only a single component can be improved at a time. In addition, the construction of atoms requires accurate estimation of the instantaneous frequency of the signal component. For components with complex and adjacent components, it is difficult to accurately extract the instantaneous frequency of a single signal, which affects the resolution of parametric time-frequency analysis.

[0003] There are a large number of non-stationary signals in production and life, and time-frequency analysis is needed to give the time-frequency distribution of the signal and obtain the relationship between the instantaneous frequency and instantaneous amplitude of each component and time. For example, human voice signals or animal call signals need to be analyzed in audio analysis software, and vibration signals of changing working conditions need to be analyzed in rotating machinery state detection systems. So far, there is no time-frequency analysis method using parametric resampling. Summary of the invention

[0004] For multi-component non-stationary signals such as sound signals and vibration signals, the present invention proposes a high-resolution time-frequency analysis method based on parametric resampling to address the problems that the existing technology cannot process multi-component signals to achieve synchronous improvement of time-frequency resolution, high-resolution time-frequency analysis of complex component signals, and multi-component signals have multiple instantaneous frequencies while parametric time-frequency analysis can only improve the resolution of a single component at a time. The method can extract the relative trends shared by multiple component components from complex multi-component signals, thereby realizing parametric resampling time-frequency analysis, synchronously improving the time-frequency resolution of each component, and is not affected by densely adjacent complex components. It has good noise resistance and can obtain accurate and high-resolution time-frequency distribution.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a high-resolution time-frequency analysis method based on parameterized resampling for multi-component non-stationary signals. The method calculates the relative fluctuation spectrum of an input signal and extracts a ridge line therefrom to estimate a relative trend function. The parameterized resampling function is then expressed by a kernel function obtained by fitting the relative trend function. Time-frequency analysis is then performed based on the resampling function to obtain a high-resolution time-frequency distribution of the multi-component non-stationary signal.

[0007] The present invention relates to a system for implementing the above method, comprising: a relative trend function estimation unit, a parameterized resampling function construction unit and a parameterized resampling time-frequency analysis unit. The relative trend function estimation unit calculates the relative fluctuation spectrum, extracts the ridge line, and estimates the relative trend function of the instantaneous frequencies of multiple component components according to the input signal. The parameterized resampling function construction unit obtains the kernel parameters by fitting the specified kernel function form according to the common trend function, and then constructs the parameterized resampling function. The parameterized resampling time-frequency analysis unit obtains the high-resolution time-frequency distribution through the parameterized resampling time-frequency transformation according to the parameterized resampling function. The time-frequency distribution can be used for the calculation of the relative fluctuation spectrum to obtain a relative trend function with higher accuracy until the iteration converges.

[0008] Technical Effects

[0009] The present invention uses a relative fluctuation spectrum and a relative trend function extraction method of a relative trend function estimation unit. Compared with other time-frequency distributions that present the changing relationship between the instantaneous frequencies of each component over time, the relative fluctuation spectrum extracts the common trend of the instantaneous frequencies of all components, is not interfered by complex and dense components, and has good noise resistance. The extracted relative trend function is not the instantaneous frequency of a single component, but a common feature of all components. The present invention uses the frequency telescoping effect of time domain resampling through the parametric resampling time-frequency transformation in the parametric resampling time-frequency analysis unit, and can construct time-frequency atoms that adapt to different components for multi-component signals at the same time. Compared with traditional parametric time-frequency analysis, it can simultaneously improve the time-frequency resolution of all components, and does not need to decompose the signal, thus avoiding the error caused by decomposition. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a flow chart of the present invention;

[0011] Figure 2 This is a schematic diagram of the relative fluctuation spectrum calculation principle in step 1 of the embodiment;

[0012] Figure 3 Schematic diagram of relative fluctuation spectrum obtained in the embodiment;

[0013] Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 , Fig.10 , Fig.11 It is a schematic diagram of the effect of the embodiment. DETAILED DESCRIPTION

[0014] like Figure 1 As shown, this embodiment relates to a high-resolution time-frequency analysis method based on parameterized resampling, including:

[0015] Step 1, calculate the relative fluctuation spectrum of the input signal and estimate the common change trend of the instantaneous frequencies of multiple components;

[0016] like Figure 2 As shown, the relative fluctuation spectrum of the input signal The relative fluctuation spectrum is used to extract the common characteristics of the instantaneous frequency of multi-component signals, namely the relative trend function. The extraction process comprehensively utilizes all component components without being disturbed by complex and dense adjacent components, that is, the ridge line v(t) of the relative fluctuation spectrum is extracted and the relative trend function shared by multi-component signals is estimated. Where: c is the unknown coefficient, cov(·) is the covariance, σ(·) is the standard deviation, and the relative fluctuation spectrum is a two-dimensional distribution about t and α; and By short-time Fourier transform and Instantaneous spectrum amplitude at two moments and The ω variable in is scaled by coordinates, t is the time point, and Δt is the time interval.

[0017] The instantaneous frequency Where: g σ (τ-t0) is the window function; multi-component signal i = 1, 2, ..., N, where: s i (t) is the i-th signal component; a i (t)>0 and n i f(t) is the instantaneous amplitude and instantaneous frequency of the component. The instantaneous frequency of each frequency is determined by a common relative trend function f(t) that varies with time and a constant n for each component. i This is obtained by multiplying, which conforms to the relationship satisfied by the instantaneous frequencies of each component of multi-component signals such as sound signals and mechanical vibration signals.

[0018] like Figure 3 The following is an example of the relative fluctuation spectrum obtained by simulating a signal, where the input signal is: f(t) = 2t 2 -4t+3, The signal is a coupled signal with six components with the same trend.

[0019] Step 2: Use the common change trend to construct a parameterized resampling function to construct a parameterized resampling time-frequency transform, that is, according to the relative trend function obtained in step 1, use Obtain the parameters of the kernel function and then determine the parameterized resampling function r P (t).

[0020] The parameters of the kernel function are: the relative trend function is characterized as a parameterized relative trend function using the kernel function: P (t) = c·κ P (t), where: parameter To ensure that the length of the signal in the time domain and pseudo-time domain is consistent, Wherein: the coordinate variable for the pseudo time domain is ψ, and its mapping relationship with the time domain coordinate variable t is: ψ=r(t), r(·) is the resampling function, which characterizes the mapping relationship between the time domain and the pseudo time domain, and is defined here as a monotonically increasing function.

[0021] The parameterized resampling function Among them: The kernel function represented by the parameter set P is κ P , the kernel function κ P It can be represented by a polynomial function: a0, ..., a n} is the polynomial coefficient, n is the polynomial order; the kernel function κ P Using Fourier technology, it can be characterized as: Where: {a0,…,a n , b1, ..., b n} is the coefficient of the Fourier series, and n is the order of the Fourier series. Using the redundant Fourier model, let To eliminate the influence of Runge effect.

[0022] The parameterized resampling function can also be calculated using the instantaneous frequency of a single signal component, specifically: the time-frequency distribution of the signal is calculated by short-time Fourier transform, one of the multiple components is manually selected, or the component with the largest energy is selected, its time-frequency ridge is extracted, and its instantaneous frequency is estimated. This instantaneous frequency can also be used as the relative trend function estimated above

[0023] Step 3: Use the parameterized resampling function to perform parameterized resampling time-frequency analysis, specifically: in: ψ=r P (τ) is a rotation and scaling transformation, which is to scale the frequency axis by resampling to achieve the rotation of multiple components. The goal is to demodulate multiple non-stationary components into stationary components at the same time; θ = r P ′(t0)ψ is a translation and scaling transformation, which is to scale the frequency axis through resampling to achieve translation of multiple components. The goal is to move multiple rotated signal components back to their original frequency positions at the same time. By performing translation and scaling transformations and rotation and scaling changes on the signal, time-frequency atoms that are adapted to the time-frequency characteristics of the multi-component signal are constructed, which can greatly reduce the influence of the time-frequency uncertainty principle and obtain a high-resolution time-frequency representation of the multi-component signal that is superior to the traditional time-frequency analysis method. Different from the original modulation and demodulation-based parametric time-frequency analysis, the parametric resampling time-frequency analysis is based on resampling and can simultaneously improve the time-frequency resolution of multiple components with the same trend.

[0024] The parameterized resampling time-frequency analysis described above, when the kernel function is a polynomial kernel, is specifically: in:

[0025]

[0026] The parameterized resampling time-frequency analysis described above, when the kernel function is a Fourier kernel, is specifically: in:

[0027]

[0028] By using the parameterized resampling time-frequency transform, a time-frequency distribution with higher time-frequency resolution can be obtained. The new time-frequency distribution can be used to replace the short-time Fourier transform in step 1 to obtain a new relative fluctuation spectrum, estimate a more accurate relative trend function, construct a parameterized resampling function, and then obtain a new parameterized resampling time-frequency analysis until the iteration converges. The convergence judgment condition is: Where: ξ is a given threshold, f i and f i- are the relative trend functions estimated for the current and previous times respectively.

[0029] After specific practical experiments, the method of the present invention is used to obtain the time-frequency distribution of multi-component non-stationary signals for the vibration signal under the variable speed working condition of the gearbox. The sampling frequency is 20kHz, and the sampling is downsampled to 2kHz. The signal window width is set to 1024 points, and the time interval of the relative fluctuation spectrum is selected as 50 data points. Figure 4 As shown in Figure 1, it is the relative fluctuation spectrum of the vibration signal constructed under the variable speed working condition of the multi-gearbox transmission system. The relative trend function is fitted by a second-order polynomial function, as shown in Figure 1. Figure 5 As shown in Figure 1, the relative trend function is obtained by fitting the resampling function using the polynomial kernel. The error threshold is set to 0.002. After multiple iterations, the algorithm finally converges, as shown in Figure 1. Figure 6 As shown in the figure, it is an example of the result of parameterized resampling time-frequency transformation of the vibration signal. For comparison, Figure 7 The results of other time-frequency distribution calculation methods are given, among which (a) and (b) are the time-frequency distributions obtained by short-time Fourier transform and continuous wavelet transform respectively. It can be seen that their time-frequency resolution is limited, especially in the high-frequency part where the energy concentration is low. (c) is the time-frequency distribution obtained by Wigner distribution. It can be seen that the interference of cross terms is serious, which damages the readability of the time-frequency distribution. (d) is the time-frequency distribution obtained by the rearrangement spectrum method. It can be seen that there are many noise points, which affects the readability of the signal. (e) is the time-frequency distribution obtained by the parametric demodulation time-frequency analysis method. Since this method is only effective for a single component at a time, it cannot improve the time-frequency resolution of multiple components at the same time.

[0030] After specific practical experiments, the method of the present invention is used to obtain the time-frequency distribution of multi-component non-stationary signals for a human voice signal intercepted from a song. The sampling frequency is 48kHz, and it is downsampled to 9.6KHz. The signal window width is set to 1024 points, and the time interval of the relative fluctuation spectrum is selected to be 50 data points. Figure 8 As shown in the figure, it is a relative fluctuation spectrum constructed from a singing audio signal; the relative trend function is fitted using the 40th order Fourier kernel function as shown in the figure. Fig. 9As shown in the figure, the relative trend function is obtained by fitting the resampling function constructed using the Fourier kernel. The error threshold is set to 0.002. After multiple iterations, the algorithm finally converges, as shown in the figure below. Fig.10 As shown in the figure, it is an example of the result of parameterized resampling time-frequency transformation of the sound signal. For comparison, Fig.11 The results of other time-frequency distribution calculation methods are given, among which (a) and (b) are the time-frequency distributions obtained by short-time Fourier transform and continuous wavelet transform respectively. It can be seen that their time-frequency resolution is limited, especially in the high-frequency part where the energy concentration is low. (c) is the time-frequency distribution obtained by Wigner distribution. It can be seen that the interference of cross terms is serious, which damages the readability of the time-frequency distribution. (d) is the time-frequency distribution obtained by the rearrangement spectrum method. It can be seen that there are many noise points, which affects the readability of the signal. (e) is the time-frequency distribution obtained by the parametric demodulation time-frequency analysis method. Since this method is only effective for a single component at a time, it cannot improve the time-frequency resolution of multiple components at the same time.

[0031] Compared with the existing technology, this method can extract the relative trends common to multiple component components from complex multi-component signals, thereby realizing parametric resampling time-frequency analysis, and can simultaneously improve the time-frequency resolution of each component. It is not affected by densely adjacent complex components, has good anti-noise performance, and can obtain accurate and high-resolution time-frequency distribution.

[0032] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A high-resolution time-frequency analysis method based on parametric resampling, characterized in that: include: Step 1, calculate the relative fluctuation spectrum of the input signal and estimate the common change trend of the instantaneous frequencies of multiple components; Step 2: Use the kernel function obtained from the common change trend to construct a parameterized resampling function to construct a parameterized resampling time-frequency transform, that is, according to the relative trend function obtained in step 1, use Obtain the parameters of the kernel function and then determine the parameterized resampling function r P (t); Step 3, use the parameterized resampling function to perform parameterized resampling time-frequency analysis to obtain the high-resolution time-frequency distribution of the multi-component non-stationary signal, specifically: in: ψ=r P (τ) is a rotation and scaling transformation, which is to scale the frequency axis by resampling to achieve the rotation of multiple components; The parameterized resampling time-frequency analysis described above, when the kernel function is a polynomial kernel, is specifically: in: The relative fluctuation spectrum of the input signal The relative fluctuation spectrum is used to extract the common characteristics of the instantaneous frequency of multi-component signals, namely the relative trend function. The extraction process comprehensively utilizes all component components without being disturbed by complex and dense adjacent components, that is, the ridge line v(t) of the relative fluctuation spectrum is extracted and the relative trend function shared by multi-component signals is estimated. Where: c is the unknown coefficient, cov(·) is the covariance, σ(·) is the standard deviation, and the relative fluctuation spectrum is a two-dimensional distribution about t and α; and By short-time Fourier transform and Instantaneous spectrum amplitude at two moments and The ω variable in is scaled by coordinates, t is the time point, Δt is the time interval; The instantaneous frequency Where: g σ (τ-t0) is the window function; multi-component signal Where: s i (t) is the i-th signal component; a i (t)>0 and n i f(t) is the instantaneous amplitude and instantaneous frequency of the component. The instantaneous frequency of each frequency is determined by a common relative trend function f(t) that varies with time and a constant n for each component. i Multiply together.

2. The high-resolution time-frequency analysis method based on parametric resampling according to claim 1 is characterized in that: The parameters of the kernel function are: the relative trend function is characterized as a parameterized relative trend function using the kernel function: P (t) = c·κ P (t), where: parameter To ensure that the length of the signal in the time domain and pseudo-time domain is consistent, Wherein: the coordinate variable for the pseudo time domain is ψ, and its mapping relationship with the time domain coordinate variable t is: ψ=r(t), r(·) is the resampling function, which characterizes the mapping relationship between the time domain and the pseudo time domain, and is defined here as a monotonically increasing function.

3. The high-resolution time-frequency analysis method based on parametric resampling according to claim 1 is characterized in that: The parameterized resampling function Among them: The kernel function represented by the parameter set P is κ P , the kernel function κ P It can be represented by a polynomial function: {a0,…,a n } is the polynomial coefficient, n is the polynomial order; the kernel function κ P Using Fourier technology, it can be characterized as: Where: {a0,…,a n ,b1,…,b n } is the coefficient of the Fourier series, n is the order of the Fourier series, and the redundant Fourier model is used. To eliminate the influence of Runge effect.

4. The high-resolution time-frequency analysis method based on parametric resampling according to claim 1 is characterized in that: Calculate the instantaneous frequency of a single signal component to realize the calculation of the parameterized resampling function. Specifically, calculate the time-frequency distribution of the signal through short-time Fourier transform, select a component component or a component component with the largest energy among multiple components, extract its time-frequency ridge, and estimate its instantaneous frequency as the relative trend function.

5. The high-resolution time-frequency analysis method based on parametric resampling according to claim 1 is characterized in that: The parameterized resampling time-frequency analysis described above, when the kernel function is a Fourier kernel, is specifically: in:

6. A high-resolution time-frequency analysis system based on parametric resampling for implementing any of the methods described in claims 1 to 5, characterized in that: include: A relative trend function estimation unit, a parameterized resampling function construction unit and a parameterized resampling time-frequency analysis unit, wherein the relative trend function estimation unit calculates the relative fluctuation spectrum, extracts the ridge line, and estimates the relative trend function of the instantaneous frequencies of multiple component components based on the input signal; the parameterized resampling function construction unit obtains the kernel parameters by fitting the specified kernel function form based on the common trend function, and then constructs the parameterized resampling function; the parameterized resampling time-frequency analysis unit obtains a high-resolution time-frequency distribution through parameterized resampling time-frequency transformation based on the parameterized resampling function, and the time-frequency distribution can be used for calculating the relative fluctuation spectrum to obtain a relative trend function with higher accuracy until the iteration converges.

7. The high-resolution time-frequency analysis system based on parametric resampling according to claim 6 is characterized in that: The convergence judgment condition is: Where: ξ is a given threshold, f i and f i-1 are the relative trend functions estimated for the current and previous times respectively.

Images